How are cycles lamp types different?
Generally, a high view factor between your scene and the lamp you use makes sampling smoother and less noisy, but also reduces the contrast in your scene. 

Therefore, point lamps and sun lamps are relatively inefficient, meshlights and other lamps with a significant and homogenous surface area are more efficient and ambient light from an environment map (that has a low contrast or at least not only small points of light on it) is the most efficient lighting source.

While the lamp choice has relatively significant effects on the noise produced in combination with glossy and glass surfaces (especially with caustics enabled), the influence is smaller with matte surfaces.

The "Multiple Importance Sample" option in materials and lamps optimizes the sampling for small view factors and thereby (partially) compensates for the inefficiencies created by them.